In this section we provide results for the mean-square end-to-end distance for a semiflexible polymer enclosed inside of a cube domain. All the problem is reduced to solve the Neumann eigenvalue problem \(-\nabla ^2\psi =\lambda \psi \)  with Neumann boundary condition when the compact domain is \(\mathcal {C}:=\left\lbrace (x,y,z)\in \mathbb {R}^{3}: 0\le x\le a, 0\le y\le a, 0\le z\le a \right\rbrace \)  is a cube of side \(a\)  in the positive octant. This problem is widely studied in different mathematical physics problems [1]}, [2]}. The eigenfunctions in this case can be given by
\(\psi _{\bf k}\left({\bf R}\right)=\frac{N_{nmp}}{a^{3/2}}\cos \left(\frac{\pi n}{a}x\right)\cos \left(\frac{\pi m}{a}y\right)\cos \left(\frac{\pi p}{a}z\right),\) 
